Finding the x-Intercept of a Perpendicular Line Passing Through a Given Point

[MrNeWBiE]

Homework Statement

Find the x-intercept of the line that passes through the point (1; 2) and perpendicular to the
line joining (1; 1) and (3; 4):

The Attempt at a Solution

I want to confirm my steps if it's right ,,,,

M=(4-1)/(3-1)= 3/2

y-1=3/2(x-1) ====> y=(3/2)x-1/2

perpendicular = m1xm2=-1 ====> m2=-2/3

y-2=-2/3(x-1) ====> y=(-2/3)x+4/5


making it one equation

(3/2)x-(1/2)=(2/3)x+(4/3)
x=11/13

 

[benhou]

making it one equation

(3/2)x-(1/2)=(2/3)x+(4/3)
x=11/13

I am not sure what you did here. I am assuming you were trying to combine the equation of the first line with the second line. If so, you have calculated the point of intersection of the two lines, which is not what the question has asked for. The question asked you for the x-intercept of the line.

 

[MrNeWBiE]

aha ,,,
so I should not combine them ,,,

(-2/3)x+4/5 = 0 ?

and the answer will be (10/13,0)

 

[benhou]

Looks good to me!

 

[MrNeWBiE]

ops ,,,
I had a mistake in y=(-2/3)x+4/5 ,,, should be y=(-2/3)x+8/3

the answer is (4,0) ,,,

btw the for your helping